A Generalized Potential with Adjustable Slope: A Hydrostatic Alternative to Cluster Cooling Flows

Abstract

I discuss a new gravitational potential, Phi(r) ~ (r_0^n+r^n)^(-1/n), for modeling the mass distribution of spherical systems. This potential has a finite mass and generates a density profile with adjustable inner slope 2-n. A gas embedded in this potential has hydrostatic temperature and gas density distributions that are elementary functions of n, greatly simplifying the task of measuring the slope from X-ray data. I show that this model is successful in describing the rising temperature profile and steep gas density profile often seen in cooling flow clusters. An application to the Abell 478 cluster of galaxies yields an inner slope 2-n = 1.0 +/- 0.2 (90%), consistent with the inner regions of collisionless dark matter halos first simulated by Navarro, Frenk, and White. The potential is also useful for cluster dynamics: it is a generalization of the familiar Hernquist and Plummer potentials, and because it is invertible, it allows for easy analytic calculation of particle phase space distribution functions in terms of n.